As semiconductor geometries continue to shrink, manufacturers have increasingly turned to optical techniques to perform non-destructive inspection and analysis of semiconductor wafers. Optical techniques typically apply an incident field (often referred to as a probe beam) to a sample and then detect and analyze the reflected energy. This type of inspection and analysis is known as optical metrology and is performed using a range of optical techniques. Scatterometry is a specific type of optical metrology that is used when the structural geometry of a sample creates diffraction (optical scattering) of the incoming probe beam. Scatterometry systems analyze diffraction to deduce details of the structures that cause the diffraction to occur.
Various optical techniques have been used to perform optical scatterometry. These include broadband spectroscopy (U.S. Pat. Nos. 5,607,800; 5,867,276 and 5,963,329), spectral ellipsometry (U.S. Pat. No. 5,739,909) single-wavelength optical scattering (U.S. Pat. No. 5,889,593), and spectral and single-wavelength beam profile reflectance and beam profile ellipsometry (U.S. Pat. No. 6,429,943). In addition it may be possible to employ single-wavelength laser BPR or BPE to obtain critical dimension (CD) measurements on isolated lines or isolated vias and mesas. The above cited patents and patent applications, along with PCT Application No. WO03/009063, U.S. Publication No. 2002/0158193, U.S. Publication No. 2003/0147086, U.S. Publication No. 2001/0051856 A1, PCT Application No. WO 01/97280, U.S. Pat. No. 6,483,580, PCT Application No. WO 02/27288 and PCT Application No. WO 03/054475 are all incorporated herein by reference.
As shown in FIG. 1, a typical scatterometry system includes an illumination source that creates a mono or polychromatic probe beam. The probe beam is preferably focused by one or more optical components (lenses in this case) to create an illumination spot on the surface of the sample under test. A second series of optical components (lenses for this example) transports the diffracted probe beam to a detector. The detector captures the diffracted energy and produces corresponding output signals. A processor analyzes the signals generated by the detector using a database.
Scatterometry systems (like the one shown in FIG. 1) may be used to analyze a wide range of samples. A typical example, shown in FIG. 2, includes a scattering structure formed on a substrate. For this particular example, the scattering structure is a grating composed of a series of individual lines. In general, the scattering structure may be periodic (as in the case of FIG. 2) or isolated. Isolated structures include, for example individual lines or individual vias. The scattering structure of FIG. 2 is uniform (i.e., exhibits translational symmetry) along the Y axis. For this reason, the scattering structure is considered to be two-dimensional. Three dimensional scattering structures are also possible both in isolation (e.g., single via) or periodically (e.g., pattern of vias). The scatting structure is covered by an incident medium that is typically air but may be vacuum, gas, liquid, or solid (such as an overlaying layer or layers). One or more layers may be positioned between the scattering structure and the substrate. In most cases, the probe beam intersects the scattering structure at a normal angle (i.e., perpendicular to the lines that from the scattering structure). Conical scattering, where the probe beam intersects the scattering structure at a non-normal angle is also possible.
In most cases, a modeling process is used to translate the empirical measurements obtained during scatterometry into physical measurements such as line widths. For this process, a software model is used to represent the expected structure and composition of the sample. The software model is parameterized, allowing characteristics such as line widths and line profiles to be changed. Maxwell's equations are used to predict the diffraction that the modeled structure would impart to the probe beam of the scatterometer. A set of these predicted measurements are generated using variations to the parameters of the model. This process is repeated until the predicted measurements match the empirical measurements to a desired goodness of fit. At that point, the modeled structure and its associated parameters are assumed to match the sample.
To be accurate, the model used during the modeling process must reflect the structure and composition of the sample. For the example of FIG. 2, this can be relatively straight-forward. The lines of the scattering structure in that example are rectangular in cross-section, allowing each line to be modeled using a small number of parameters (typically, line height and line width). Each line is further simplified by being composed of a single material and being geometrically invariant along the Y-axis. In practice, this relative simplicity is not always typical of samples. FIG. 3 shows, for example a sample that includes lines having rounded edges and sloping sidewalls. Adding additional complexity, the lines in the scattering structure of FIG. 3 are composed of multiple layers, each of which may have different dielectric properties.
Complex samples, such as the sample shown in FIG. 3 require correspondingly complex modeling techniques. For one of these techniques, a Riemannian approach is used to model geometric shapes (such as the lines) as stacks of slabs. For example, the line profile of FIG. 4A may be modeled using the stack of slabs shown in FIG. 4B. The height and width of each slab is chosen so that the stack of slabs approximates the shape being modeled. Portions of the shape that change rapidly (such as the foot or top of the line profile of FIG. 4A) can be accurately modeled by increasing the number of slabs while decreasing their thickness (not shown). Shape portions that are relatively constant may be modeled using fewer, thicker slabs. Models constructed using this technique require two parameters for each slab (height, width) or a total of 2N parameters for N slab models.
The slab-based technique necessarily introduces a degree of roughness into the resulting model. This roughness gives the model edges a staircase-like appearance attributable to the rectangular cross-section of the individual slabs. This side-effect can be reduced by using slabs that have a trapezoidal cross-sections or quadrilateral cross-sections. The use of trapezoid slabs is shown in FIG. 4C. The overall effect is a reduction in stair-stepping at the cost of additional parameters. For trapezoidal cross-sections, three parameters are required for each slab (height, width and one interior angle). Quadrilateral cross-sections require four parameters (height, width and two interior angles).
Quadrilaterals or trapezoids are an effective method for increasing the accuracy of the modeling process. At the same time, the increased number of parameters adds further complexity to an already arduous computational process. As a result, there are continuing efforts to find modeling methods that provide high accuracy while limiting the number of required parameters. This is the goal of the method described, for example in U.S. Pat. No. 5,963,329 (incorporated in this document by reference). For this method, the familiar slab-based approach is used to model lines and other geometric shapes. In this case, however, the slabs are subdivided into one or more sub-profiles. Each sub-profile has a reference edge and a reference height. The width of each slab in a sub-profile is defined using an offset (which may be positive or negative) from the reference edge. The height of each slab in a sub-profile is defined as a multiple of the reference height. Each sub-profile also has two scaling factors, one for height and a second for width. Changing the height scaling factor increases or decreases the height of all of the slabs in a sub-profile making the sub-profile taller or shorter. Changing the width scaling factor spreads the sub-profile—slabs that are narrower than the reference edge become narrower still, slabs that are wider than the reference edge become even wider. By controlling the scaling factors for each sub-profile, the overall profile of the line can be varied to produce a range of differing shapes.
The use of sub-profiles and associated scaling factors decreases the number of parameters that are required to define a particular shape. Unfortunately, the use of rectangular slabs suffers from the staircase limitations already described. It is also true that the use of scaling factors is only beneficial when computational results can be re-used as the scaling factors are changed. For cases where this is not possible, the use of scaling factors is computationally similar to more traditional methods for defining slab heights and widths.
For these reasons and others, a need exists for scatterometry techniques that avoid the limitations of traditional modeling methods. This need is particularly apparent for high density semiconductor wafers where feature sizes are small.